Tonight I leave for Sydney, Australia and I will arrive early Thursday morning. The event I am attending kicks off Friday. I plan to sleep as much as I can on the flights (I am good at sleeping on planes) and to spend Thursday sightseeing. I want to be outside and at least slightly active (walking around looking at things and taking pictures) since this is one of my anti-jetlag strategies but not strenuous (climbing things, committing to a long hike). I need to be able to bail at any time to go have a nap if I am just unworkably tired.

A perfect itinerary would involve 5 or 6 buildings or destinations to look at that require 2 or 3 hours worth of walking, so that with a certain amount of standing around looking at things and going into places, I've spent 6 or 8 hours doing it. I am a huge museum fan normally, but unless it's super amazing that wouldn't be my choice for this day. Ditto movies, restaurants you sit in while eating a two hour meal, etc. I'll be in Sydney for over a week and have some other free time (and some people to spend it with) so this day is best for things a solo traveller would enjoy, even if not entirely awake.

I'm staying at the Four Points Darling Harbour which I think is a pretty good base for a walking tour. But I have no plan right now other than putting on sunscreen and heading out the door with my camera and some cash for a taxi back to the hotel when I'm tired.

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6 Answers
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Given you're staying in the city and have time restrictions, I'd suggest remaining the CBD generally, but here's the route I'd take if I was "showing off" Sydney (albeit in the opposite direction to what I've ended up with on Google Maps).

I'm going to list a lot of stuff below, more so that you can pick and choose anything of interest. Following that map around you'd have the option of seeing stuff like:

Sydney Aquarium and Wildlife - As someone who makes a habit of seeing aquariums when he travels (funny habit, I know), Sydney is one of the best I've seen. The Wildlife area is new, but very good if you're not going to get outside Sydney but still want to see some of our native wildlife.

The Chinese Gardens - Not a huge attraction, just a nice quiet place to relax in for a short while.

The Queen Victoria Building - One of Sydney's most unique buildings, this is an arcade in an old Victorian era building. Boutique shopping, but to me the main attraction is the building itself.

Pitt Street Mall - Not something I'd recommend myself, but it's there in between these two. Mainly nondescript shopping arcades leading off it.

Centrepoint Tower - A great view of Sydney in good weather, this is the huge tower that stands over Sydney.

Hyde Park, Archibald Fountain and the ANZAC Memorial - A bit of greenery in our inner city, with an unusual fountain plus our war memorial. You can also catch a bus from beside Hyde Park to iconic Sydney beaches like Bondi or Coogee.

St Mary's Cathedral - An interesting combination of an English-style gothic church in local Sydney sandstone.

St James' Church - The oldest existing church building in Sydney, designed by our first recognized architect.

Hyde Park Barracks and Museum - The building itself is interesting, dating from the early colonial days of Sydney. I haven't actually checked out the museum itself.

Art Gallery of NSW - One of the few museums I'd recommend given your comments. It has quite an eclectic collection, including plenty of Australian art. Free entry, and being quite small it can be a half hour to hour visit.

Sydney Botanic Gardens - Worth a wonder through on your way from the art gallery to Circular Quay, it's also a destination in its own right. It also contains NSW's Government House - home to the governor and a historic building in its own right.

Mrs Macquarie's Chair - Down the end of a small peninsula in the harbour, the end gives you views throughout the harbour. Quite a pretty sight-seeing stop and walk through the Botanic Garden to get there.

Sydney Opera House - Iconic. My wife swears by the backstage tours that they do, if you're interested in learning more about the building itself.

Circular Quay - Not of great interest in and of itself, as it's neither particularly historic or pretty. Customs House, just behind it, is impressive looking. You can also catch ferries from here to Taronga Zoo (though that's a day trip in itself) or to Manly (the Manly ferry is more the experience than Manly itself, which is just another beach suburb).

Museum of Contempory Art - This depends on your opinion of contemporay art. I'd skip it but some people love it, so I'll include it here.

The Rocks - This is the area behind the MCA. It's got plenty of history and you could easily waste an hour or more wandering its streets. There are a number of displays that give interesting tidbits about the area scattered around.

The Sydney Harbour Bridge/Bridge Climb/Pylon Climb - I'm not a huge fan of the Bridge Climb personally but I know plenty of people who are. It's definitely an experience you're not getting anywhere else, but if you don't feel like doing the whole thing there's the cheaper option of a pylon climb for similar views.

And then back to your hotel...

If it was me with your comments above, I'd see the Aquarium/Wildlife, QVB, go up Centrepoint Tower, walk through Hyde Park and past the fountain and ANZAC Memorial, the Art Gallery, walk through the Botanic Gardens and the backstage tour of the Opera House.

In the end I agreed to meet other people, whose planes came in a few hours later, and then there was some mussing around getting lunch etc. We spent the afternoon at Sydney Wildlife / Aquarium and it was a good pace for our tiredness. For that reason I'll accept this one, but I'm hoping to use the suggestions from ALL the answers as the week progresses...
– Kate GregoryJul 5 '12 at 11:20

I took this tour in April 2011 and would recommend it. It gave a nice overview of Sydney's main sights and history, along with a good dose of interesting anecdotes and self-mocking Australian humour. :-) It's perfect for a solo traveller too.

NB: the tour is indeed free if you want, but at the end the guide will ask everyone to chip in with a small tip / donation; most people choose to do so.

Edit: Why I think this might work nicely for your groggy day sightseeing:

No need to think so much; just follow the tour. :-) (Potentially a plus if you're tired.)

If you can make the 10:30 am tour, by early afternoon you'll have had a cursory look at the main sights in central Sydney, and can spend the rest of the day further investigating the most interesting bits. For example, after the tour ends near Circular Quay, grab some lunch and head for the Opera House for a closer look; it's not far and the waterfront is pleasant for walking.

If, for whatever reason, you're not fully enjoying the tour, you can drop out anytime and continue at your own pace.

Since you've done it, when it says you'll "see" Fort Denison, I assume that means from the shore?
– dlanodJul 3 '12 at 22:00

Yeah, from the shore. Same with the Opera House—we only saw it from a vantage point near the Circular Quay (this place, if I recall right). Only so much fits in a 3-hour walk, but I think it's a good overview: you can later go and visit the places you found most interesting with more time.
– JonikJul 3 '12 at 22:16

Cheers. Being a Sydney-sider myself, I've seen those walking tours going around and have been tossing up going on them recently myself (I'm not a native, so my knowledge is sporadic), hence the question.
– dlanodJul 3 '12 at 22:45

Sydney is one of my favorite cities, and has a ton to offer. A single day just wouldn't do it justice, as that can be the amount of time you'd spend just watching one of the many attractions. Here is a list from memory, which would suit your sightseeing preferences:

The Darling Harbor - The place you are staying is the tourist hub and provides great walking spaces and restaurants around the pier.

The Opera House - Catch an evening performance and get there early to soak in this magnificent structure. Also adjoining are the Botanical Gardens, if you have time.

The famed Sydney Harbor Bridge. Consider the bridge climb to get up close and intimate with this gorgeous structure.

I think these 3 top attractions, in my opinion, would fill your day. Also consider the Bondi Beach area for good restaurants. Fantastic for people and home spotting.

Since you are travelling alone, and will have time to explore later, I would recommend taking the hop-on/hop-off bus tour, for the solo day, which will provide you a comprehensive primer on most of what Sydney has to offer. You can always revisit the places that were most appealing.

If you're going from Darling Harbour to the Harbour Bridge, then I'd suggest detouring via the Rocks. The Rocks Discovery Museum is well worth a visit there - interesting history of Sydney and the area, plus it's free!
– GagravarrJul 4 '12 at 11:21

I live in Sydney and when we have guests come we split the city up into 2 day trips. One of these focuses on the area close to Darling Harbour the other near Sydney Harbour Bridge and Opera House.

My suggestion is for the second option, as you will be able to get a good glimpse of Darling Harbour from your hotel. The bridge and its surrounds are supposed to be Sydney's main attraction; it would be a shame to miss.

From your hotel (I am assuming is the Four Points Sheraton), walk up King St until you hit George Street. From there you should be able to get either a bus or taxi very easily. Ask to be taken to Circular Quay (most buses going on George St are going to Circular Quay).

From Circular Quay walk along the foreshore until you reach the Opera House. Here you will get plenty of opportunities to take nice photos of the bridge and also the Opera House.

You can go inside the main entrance of the Opera House and walk to the first level (a flight of steps) then walk outside some glass doors to your left you can get some good pics of the bridge from there.

Walk down the large steps surrounding the Opera House forecourt and head down and to your left towards the entrance to the Botanical Gardens.

When you walk in through the gates of the gardens, don't follow the waters edge (maybe you can take some photos along the shore then head back to the entrance). There is a path that goes up and to the right (it is more the middle as there is another path that goes up and does a sharp right turn and loops back on itself, don't follow this). If you are on the right path you will see this lovely big fig tree https://ssl.panoramio.com/photo/53022858 that everyone likes to take photos of.

Keep following the path until you come to a junction, you want to take the Macquarie St exit (see the little green sign in the center of this map which says Macquarie Street Exit).

From the exit it takes about 20 minutes to walk to St Mary's Cathedral (just keep following the road).

On the way to St Mary's Cathedral there are some places of interest that you may want to stop at, but don't make yourself too tired because you don't want to bomb out before you reach the Cathedral.

The Cathedral is very impressive and is open to the public (unless there is a state funeral; unlikely but this has ruined my visitor's plans once before). Inside the Cathedral photography is not allowed, but it still worth having a good look around.

Now once you have exited the cathedral it is time to assess how tired you really are. This is not a good place to buy food so I usually offer my visitors two options from here:

Get some food and then do shopping / go home

Sally forth and check out some of the other sites nearby

Heading Home

Cross the road to Hyde Park and get some photos of the Archibald Fountain. From the cathedral in a literal straight line from cathedral to fountain to other side of Hyde park you should end up and the beginning of Market St. Walk down Market street until you hit George St where there is plenty of food or just keep walking approx. 6 blocks and you will be at Sussex St where your hotel is (or get a taxi).

Keep Going

Near the entrance to the cathedral is the Fragrance Garden, a small patch of green if you are interested in that.

About 5 minutes walk; if you walk out the door of St Mary's and just keep walking straight, avoiding the fountain, and cross the road you will be at the Australian Museum. I've loved this museum since I was a kid, but not everyone loves museums, but there is one section where they have plenty of real, stuffed (dead), native animals which you could take some pictures of. They usually have some interesting stuff there.

Opposite either the church or the museum is Hyde Park. This has both the Anzac (war) Memorial and the Archibald Fountain. The fountain is definitely worth checking out.

I want more!!!

If you want to go home, go back and refer to the 'Heading Home' section above. If you still have a spring in your boots I suggest you walk to Centre Point Tower. It costs a few dollars to go in, but it is worth it for a glimpse of the city from above. You go up very high to the top of the tower and you can get a good 360 degree view of the city.

If you are still going strong, walk to George street (on the way back home) and check out the Queen Victoria building. This is an elegant building with lots of interesting (but expensive) shops.

From the QVB, walk to the North end of the QVB and you can then walk down Market street towards your hotel.

I suspect all of the above would take about 5 hours so you can decide on what you want to see or if how tired you are. I normally make this a full day when I have guests as we take a ferry in the morning from near my house and also include lunch. It is a very full day, but allows you to take in many sights.

I also suggest you take plenty of food with you as you can find yourself in certain parts of Sydney where there is not easy access to a range of food (near Hyde Park for instance). And you don't want to waste your time wandering in circles looking for a bite.

On Macquarie Street just after you pass Parliament House is Sydney Hospital. There is a small kiosk there where you can buy a meat pie or sausage roll. If you are hungry (and not a vegetarian) you could try a meat pie, this is real Aussie food, suggest getting some tomato sauce to go with the pie. Then you can tell friends you've tried some traditional Aussie food.

Also not far from the kiosk by the side of the road out the front of the hospital is a statue of this boar. Just something interesting to look at while you enjoy your pie.

Here's what I did today, Day 2. I woke up earlier than I expected, and had no duties until 11:30, so after breakfast I headed out at 8am and walked north along the Promenade until I reached the end of it. Lovely views of the bridge. Then through some streets to Observatory Park. The observatory was closed, but nice views. Then down the bridge stairs to Cumberland, looked down into the Argyle Cut, walked right under the bridge, and then down into the Rocks. Ended up looking at the Opera House and the bridge both from the same spot. Also ducked into Cadman's Cottage. Finally headed south on George and then wiggled south and west stopping in little shops along the way until I found King St and from there back to the hotel at pretty much exactly 11:30.

Then we had a few hours break this afternoon and went up the CentrePoint Tower, which isn't called that any more, it's called the Sydney Tower Eye. Fantastic views of course. So checking a lot of boxes in the first two days - and have taken about 400 photos so far :-)

I have now done the BridgeClimb. It's insanely expensive (over $200/person plus $30-50 for pics of yourself on it) but the conference provided it to us free. It takes several hours and really is astonishing. I had a great day for it. Tip: ask for the free pass to the Pylon Climb and go up there to take pictures of other people doing the bridge climb so you can show other people what you did, since you can't take your own camera on the bridge climb. You can also get pictures from the street beneath the bridge of people on the catwalks.

If you're after a museum that's not too far, is interesting and free, try the Rocks Discovery Museum. Shouldn't take too long to walk back over there, and it sounds like you missed museums out of your tour so far! The Art Gallery of NSW is also excellent and free, but quite a bit further on...
– GagravarrJul 6 '12 at 10:50

No one has suggested the blue mountains, not too far out of sydney and pretty spectacular.

And, no one has suggested the beaches, the wonderful wonderful beaches. You can walk from Bondi to Bronte, and there are also the less busy beaches on the north shore ... all great. Easily beats an aquarium.

Spoken as an englishman who spent six months in sydney,and would love to go back.

That'd be because the OP specifically stated "A perfect itinerary would involve 5 or 6 buildings or destinations to look at that require 2 or 3 hours worth of walking". Neither Blue Mountains nor beaches are really visitable in that timeframe, even ignoring the walking.
– dlanodJul 24 '12 at 21:35